Many types of medical instruments, such as an infrared (IR) thermometer, contain a probe for insertion into a body cavity so that various body related measurement can be taken. In order to prevent cross-contamination between patients, or health care workers and patients, the probe is generally enclosed within a protective cover which can be disposed of in a sanitary manner after it has been used. Typically the covers are manufactured of plastic using different types of molding techniques, many of which produce products that have surface imperfections or which cannot be held to tight tolerances. In addition, while most protective covers are packaged and shipped with the covers being stacked one inside the other, unstacking such covers and placing them upon the probe of an instrument can be extremely difficult. For example, since such covers are generally connected and/or otherwise loaded onto the medical instrument by pressing the probe onto/into the first cover in the stack, the remaining covers beneath the first probe cover tend to wedge together and/or otherwise bind in the stack with each successive loading operation. As a consequence, such probe covers can be damaged and dropped during removal from the stack. Displacement of a misshapened cover from the instrument probe during an examination can also be unnerving to both the attending health care individuals and the patient. Lastly, defective covers can hang up on the instrument during removal thus requiring unwanted manual handling of a potentially contaminated product.